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Adding Indices




 
Related Topics:
More Lessons for Arithmetic, Math Worksheets

When multiplying numbers in exponent notation with the same base, we can add the exponents.

Consider:

a2 × a3 = (a × a) × (a × a × a)
= a2 + 3
= a5

This is the first law of exponents:
am × an = am + n

Example:

Simplify the following; give your answers in exponent form

a) 33 × 32
b) x5 × x3

Solution:

a) 33 × 32 = 33 + 2
= 35
b) x5 × x3 = x5 + 3
= x8

Common Error : The first law of exponents does NOT apply to addition of numbers in exponent notation.

am + an ≠ am + n



The following video shows some examples of adding exponents.
Index rules - add and subtract indices
Basic look at the first two index laws


 

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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